Searching Elements in an Array | Array Operations
Last Updated : 23 May, 2024
In this post, we will look into search operation in an Array, i.e., how to search an element in an Array, such as:
- Searching in an Unsorted Array using Linear Search
- Searching in a Sorted Array using Linear Search
- Searching in a Sorted Array using Binary Search
- Searching in an Sorted Array using Fibonacci Search
Searching operations in an Unsorted Array using Linear Search
In an unsorted array, the search operation can be performed by linear traversal from the first element to the last element, i.e. Linear Search
Coding implementation of the search operation:
C++ // C++ program to implement linear // search in unsorted array #include <bits/stdc++.h> using namespace std; // Function to implement search operation int findElement(int arr[], int n, int key) { int i; for (i = 0; i < n; i++) if (arr[i] == key) return i; // If the key is not found return -1; } // Driver's Code int main() { int arr[] = { 12, 34, 10, 6, 40 }; int n = sizeof(arr) / sizeof(arr[0]); // Using a last element as search element int key = 40; // Function call int position = findElement(arr, n, key); if (position == -1) cout << "Element not found"; else cout << "Element Found at Position: " << position + 1; return 0; } // This code is contributed // by Akanksha Rai // C program to implement linear // search in unsorted array #include <stdio.h> // Function to implement search operation int findElement(int arr[], int n, int key) { int i; for (i = 0; i < n; i++) if (arr[i] == key) return i; // If the key is not found return -1; } // Driver's Code int main() { int arr[] = { 12, 34, 10, 6, 40 }; int n = sizeof(arr) / sizeof(arr[0]); // Using a last element as search element int key = 40; // Function call int position = findElement(arr, n, key); if (position == -1) printf("Element not found"); else printf("Element Found at Position: %d", position + 1); return 0; } // Java program to implement linear // search in unsorted arrays class Main { // Function to implement // search operation static int findElement(int arr[], int n, int key) { for (int i = 0; i < n; i++) if (arr[i] == key) return i; // If the key is not found return -1; } // Driver's Code public static void main(String args[]) { int arr[] = { 12, 34, 10, 6, 40 }; int n = arr.length; // Using a last element as search element int key = 40; // Function call int position = findElement(arr, n, key); if (position == -1) System.out.println("Element not found"); else System.out.println("Element Found at Position: " + (position + 1)); } } # Python program for searching in # unsorted array def findElement(arr, n, key): for i in range(n): if (arr[i] == key): return i # If the key is not found return -1 # Driver's code if __name__ == '__main__': arr = [12, 34, 10, 6, 40] key = 40 n = len(arr) # search operation index = findElement(arr, n, key) if index != -1: print("Element Found at position: " + str(index + 1)) else: print("Element not found") # Thanks to Aditi Sharma for contributing # this code // C# program to implement linear // search in unsorted arrays using System; class main { // Function to implement // search operation static int findElement(int[] arr, int n, int key) { for (int i = 0; i < n; i++) if (arr[i] == key) return i; // If the key is not found return -1; } // Driver Code public static void Main() { int[] arr = { 12, 34, 10, 6, 40 }; int n = arr.Length; // Using a last element as // search element int key = 40; int position = findElement(arr, n, key); if (position == -1) Console.WriteLine("Element not found"); else Console.WriteLine("Element Found at Position: " + (position + 1)); } } // This code is contributed by vt_m. // Javascript program to implement linear // search in unsorted array // Function to implement search operation function findElement( arr, n, key) { let i; for (i = 0; i < n; i++) if (arr[i] == key) return i; return -1; } // Driver program let arr = [12, 34, 10, 6, 40]; let n = arr.length; // Using a last element as search element let key = 40; let position = findElement(arr, n, key); if (position == - 1) console.log("Element not found"); else console.log("Element Found at Position: " + (position + 1)); <?php // PHP program to implement linear // search in unsorted array // Function to implement // search operation function findElement($arr, $n, $key) { $i; for ($i = 0; $i < $n; $i++) if ($arr[$i] == $key) return $i; // If the key is not found return -1; } // Driver Code $arr = array(12, 34, 10, 6, 40); $n = sizeof($arr); // Using a last element // as search element $key = 40; $position = findElement($arr, $n, $key); if ($position == - 1) echo("Element not found"); else echo("Element Found at Position: " . ($position + 1)); // This code is contributed by Ajit. ?> OutputElement Found at Position: 5
Time Complexity: O(N)
Auxiliary Space: O(1)
Searching in a Sorted Array using Linear Search
In a sorted array, the most trivial method for search operation is by using Linear Search.
Below is the implementation of the above approach:
C++ // C++ program to implement linear // search in sorted array #include <bits/stdc++.h> using namespace std; // Function to implement search operation int findElement(int arr[], int n, int key) { int i; for (i = 0; i < n; i++) if (arr[i] == key) return i; // If the key is not found return -1; } // Driver's Code int main() { int arr[] = { 5, 6, 7, 8, 9, 10 }; int n = sizeof(arr) / sizeof(arr[0]); // Using a last element as search element int key = 10; // Function call int position = findElement(arr, n, key); if (position == -1) cout << "Element not found"; else cout << "Element Found at Position: " << position + 1; return 0; } // This code is contributed // by Akanksha Rai // C program to implement linear // search in sorted array #include <stdio.h> // Function to implement search operation int findElement(int arr[], int n, int key) { int i; for (i = 0; i < n; i++) if (arr[i] == key) return i; // If the key is not found return -1; } // Driver's Code int main() { int arr[] = { 5, 6, 7, 8, 9, 10 }; int n = sizeof(arr) / sizeof(arr[0]); // Using a last element as search element int key = 10; // Function call int position = findElement(arr, n, key); if (position == -1) printf("Element not found"); else printf("Element Found at Position: %d", position + 1); return 0; } // Java program to implement linear // search in sorted arrays class Main { // Function to implement // search operation static int findElement(int arr[], int n, int key) { for (int i = 0; i < n; i++) if (arr[i] == key) return i; // If the key is not found return -1; } // Driver's Code public static void main(String args[]) { int arr[] = { 5, 6, 7, 8, 9, 10 }; int n = arr.length; // Using a last element as search element int key = 10; // Function call int position = findElement(arr, n, key); if (position == -1) System.out.println("Element not found"); else System.out.println("Element Found at Position: " + (position + 1)); } } # Python program for searching in # sorted array def findElement(arr, n, key): for i in range(n): if (arr[i] == key): return i # If the key is not found return -1 # Driver's code if __name__ == '__main__': arr = [5, 6, 7, 8, 9, 10] key = 10 n = len(arr) # search operation index = findElement(arr, n, key) if index != -1: print("Element Found at position: " + str(index + 1)) else: print("Element not found") # Thanks to Aditi Sharma for contributing # this code // C# program to implement linear // search in sorted arrays using System; class main { // Function to implement // search operation static int findElement(int[] arr, int n, int key) { for (int i = 0; i < n; i++) if (arr[i] == key) return i; // If the key is not found return -1; } // Driver Code public static void Main() { int[] arr = { 5, 6, 7, 8, 9, 10 }; int n = arr.Length; // Using a last element as // search element int key = 10; int position = findElement(arr, n, key); if (position == -1) Console.WriteLine("Element not found"); else Console.WriteLine("Element Found at Position: " + (position + 1)); } } // This code is contributed by vt_m. // Javascript program to implement linear // search in sorted array // Function to implement search operation function findElement( arr, n, key) { let i; for (i = 0; i < n; i++) if (arr[i] == key) return i; return -1; } // Driver program let arr = [5, 6, 7, 8, 9, 10]; let n = arr.length; // Using a last element as search element let key = 10; let position = findElement(arr, n, key); if (position == - 1) console.log("Element not found"); else console.log("Element Found at Position: " + (position + 1)); <?php // PHP program to implement linear // search in sorted array // Function to implement // search operation function findElement($arr, $n, $key) { $i; for ($i = 0; $i < $n; $i++) if ($arr[$i] == $key) return $i; // If the key is not found return -1; } // Driver Code $arr = array(5, 6, 7, 8, 9, 10); $n = sizeof($arr); // Using a last element // as search element $key = 10; $position = findElement($arr, $n, $key); if ($position == - 1) echo("Element not found"); else echo("Element Found at Position: " . ($position + 1)); // This code is contributed by Ajit. ?> OutputElement Found at Position: 6
Time Complexity: O(N)
Auxiliary Space: O(1)
Searching in a Sorted Array using Binary Search
In a sorted array, the search operation can be performed efficiently by using binary search.
Below is the implementation of the above approach:
C++ // C++ program to implement binary search in sorted array #include <bits/stdc++.h> using namespace std; int binarySearch(int arr[], int low, int high, int key) { if (high < low) return -1; int mid = (low + high) / 2; /*low + (high - low)/2;*/ if (key == arr[mid]) return mid; if (key > arr[mid]) return binarySearch(arr, (mid + 1), high, key); return binarySearch(arr, low, (mid - 1), key); } /* Driver code */ int main() { // Let us search 3 in below array int arr[] = { 5, 6, 7, 8, 9, 10 }; int n, key; n = sizeof(arr) / sizeof(arr[0]); key = 10; // Function call cout << "Index: " << binarySearch(arr, 0, n - 1, key) << endl; return 0; } // This code is contributed by NamrataSrivastava1 // C program to implement binary search in sorted array #include <stdio.h> int binarySearch(int arr[], int low, int high, int key) { if (high < low) return -1; int mid = (low + high) / 2; /*low + (high - low)/2;*/ if (key == arr[mid]) return mid; if (key > arr[mid]) return binarySearch(arr, (mid + 1), high, key); return binarySearch(arr, low, (mid - 1), key); } /* Driver Code */ int main() { // Let us search 3 in below array int arr[] = { 5, 6, 7, 8, 9, 10 }; int n, key; n = sizeof(arr) / sizeof(arr[0]); key = 10; // Function call printf("Index: %d\n", binarySearch(arr, 0, n - 1, key)); return 0; } // Java program to implement binary // search in a sorted array class Main { // function to implement // binary search static int binarySearch(int arr[], int low, int high, int key) { if (high < low) return -1; /*low + (high - low)/2;*/ int mid = (low + high) / 2; if (key == arr[mid]) return mid; if (key > arr[mid]) return binarySearch(arr, (mid + 1), high, key); return binarySearch(arr, low, (mid - 1), key); } /* Driver Code*/ public static void main(String[] args) { int arr[] = { 5, 6, 7, 8, 9, 10 }; int n, key; n = arr.length - 1; key = 10; // Function call System.out.println("Index: " + binarySearch(arr, 0, n, key)); } } # python 3 program to implement # binary search in sorted array def binary_search(arr, start, end, key): # if case is evaluated when element is found else -1 is returned if (start < end): mid = (start + end) //2 if (key == arr[mid]): return mid if (key < arr[mid]): return binary_search(arr, start, mid - 1, key) if (key > arr[mid]): return binary_search(arr, mid + 1, end, key) else: return -1 # Driver code if __name__ == "__main__": # Let us take a sorted array to find a key arr = [11, 20, 39, 44, 57, 63, 72, 88, 94] key = 72 index = binary_search(arr, 0, len(arr) - 1, key) if index != -1: print(f"Element found at index {index}") else: print("Element not found") # This code is contributed by Smitha Dinesh Semwal # and improved by Rahul Varma // C# program to implement binary // search in a sorted array using System; public class GFG { // function to implement // binary search public static int binarySearch(int[] arr, int low, int high, int key) { if (high < low) { return -1; } int mid = (low + high) / 2; if (key == arr[mid]) { return mid; } if (key > arr[mid]) { return binarySearch(arr, (mid + 1), high, key); } return binarySearch(arr, low, (mid - 1), key); } /* Driver Code */ public static void Main(string[] args) { int[] arr = new int[] { 5, 6, 7, 8, 9, 10 }; int n, key; n = arr.Length; key = 10; // Function call Console.WriteLine( "Index: " + binarySearch(arr, 0, n - 1, key)); } } // This code is contributed by Shrikant13 // Javascript program to implement // binary search in sorted array function binarySearch( arr, low, high, key) { if (high < low) return -1; /*low + (high - low)/2;*/ let mid = Math.trunc((low + high) / 2); if (key == arr[mid]) return mid; if (key > arr[mid]) return binarySearch(arr, (mid + 1), high, key); return binarySearch(arr, low, (mid - 1), key); } // Driver program // Let us search 3 in below array let arr = [ 5, 6, 7, 8, 9, 10 ]; let n, key; n = arr.length; key = 10; console.log("Index: " + binarySearch(arr, 0, n - 1, key) + "</br>"); <?php // PHP program to implement // binary search in sorted array function binarySearch($arr, $low, $high, $key) { if ($high < $low) return -1; $mid = (int)($low + $high) / 2; if ($key == $arr[(int)$mid]) return $mid; if ($key > $arr[(int)$mid]) return binarySearch($arr, ($mid + 1), $high, $key); return (binarySearch($arr, $low, ($mid -1), $key)); } // Driver Code // Let us search 3 in below array $arr = array(5, 6, 7, 8, 9, 10); $n = count($arr); $key = 10; // Function call echo "Index: ", (int)binarySearch($arr, 0, $n-1, $key); // This code is contributed by // Srathore ?> Time Complexity: O(log(n)) Using Binary Search
Auxiliary Space: O(log(n)) due to recursive calls, otherwise iterative version uses Auxiliary Space of O(1).
Searching in a Sorted Array using Fibonacci Search
Fibonacci Search is a comparison-based technique that uses Fibonacci numbers to search an element in a sorted array.
Below is the implementation of the above approach:
C++ // C++ program of the above approach #include <iostream> #include <vector> using std::cout; // Utility function to find minimum of two elements int minimum(int x, int y) { return (x < y) ? x : y; } /* Returns index of x if present, else returns -1 */ int fibonacciSearch(int arr[], int x, int n) { /* Initialize fibonacci numbers */ int fibMMm2 = 0; // (m-2)'th Fibonacci No. int fibMMm1 = 1; // (m-1)'th Fibonacci No. int fibM = fibMMm2 + fibMMm1; // m'th Fibonacci /* fibM is going to store the smallest Fibonacci Number greater than or equal to n */ while (fibM < n) { fibMMm2 = fibMMm1; fibMMm1 = fibM; fibM = fibMMm2 + fibMMm1; } // Marks the eliminated range from front int offset = -1; /* while there are elements to be inspected. Note that we compare arr[fibMm2] with x. When fibM becomes 1, fibMm2 becomes 0 */ while (fibM > 1) { // Check if fibMm2 is a valid location int i = minimum(offset + fibMMm2, n - 1); /* If x is greater than the value at index fibMm2, cut the subarray array from offset to i */ if (arr[i] < x) { fibM = fibMMm1; fibMMm1 = fibMMm2; fibMMm2 = fibM - fibMMm1; offset = i; } /* If x is greater than the value at index fibMm2, cut the subarray after i+1 */ else if (arr[i] > x) { fibM = fibMMm2; fibMMm1 = fibMMm1 - fibMMm2; fibMMm2 = fibM - fibMMm1; } /* element found. return index */ else return i; } /* comparing the last element with x */ if (fibMMm1 && arr[offset + 1] == x) return offset + 1; /*element not found. return -1 */ return -1; } // Driver Code int main() { int arr[] = { 10, 22, 35, 40, 45, 50, 80, 82, 85, 90, 100, 235 }; int n = sizeof(arr) / sizeof(arr[0]); int x = 235; int ind = fibonacciSearch(arr, x, n); if (ind >= 0) cout << "Found at index: " << ind; else cout << x << " isn't present in the array"; return 0; } // This code is contributed by sourabh_jain. // C program for Fibonacci Search #include <stdio.h> // Function to find minimum of two elements int minimum(int x, int y) { return (x <= y) ? x : y; } /* Returns index of x if present, else returns -1 */ int fibonacciSearch(int arr[], int x, int n) { /* Initialize Fibonacci numbers */ int fibMMm2 = 0; // (m-2)'th Fibonacci number int fibMMm1 = 1; // (m-1)'th Fibonacci number int fibM = fibMMm2 + fibMMm1; // m'th Fibonacci number /* fibM is going to store the smallest Fibonacci number greater than or equal to n */ while (fibM < n) { fibMMm2 = fibMMm1; fibMMm1 = fibM; fibM = fibMMm2 + fibMMm1; } // Marks the eliminated range from front int offset = -1; /* while there are elements to be inspected. Note that we compare arr[fibMm2] with x. When fibM becomes 1, fibMm2 becomes 0 */ while (fibM > 1) { // Check if fibMm2 is a valid location int i = minimum(offset + fibMMm2, n - 1); /* If x is greater than the value at index fibMm2, cut the subarray array from offset to i */ if (arr[i] < x) { fibM = fibMMm1; fibMMm1 = fibMMm2; fibMMm2 = fibM - fibMMm1; offset = i; } /* If x is greater than the value at index fibMm2, cut the subarray after i+1 */ else if (arr[i] > x) { fibM = fibMMm2; fibMMm1 = fibMMm1 - fibMMm2; fibMMm2 = fibM - fibMMm1; } /* element found. return index */ else return i; } /* comparing the last element with x */ if (fibMMm1 && arr[offset + 1] == x) return offset + 1; /* element not found. return -1 */ return -1; } /* driver function */ int main(void) { int arr[] = { 10, 22, 35, 40, 45, 50, 80, 82, 85, 90, 100, 235 }; int n = sizeof(arr) / sizeof(arr[0]); int x = 235; int index = fibonacciSearch(arr, x, n); if (index >= 0) printf("Element found at index: %d", index); else printf("%d is not present in the array", x); return 0; } // This code is contributed by sourabh_jain. // Java program of the above approach import java.util.*; // adding util packages class FibonacciSearch { // Function to find the minimum of two elements public static int minimum(int x, int y) { return (x <= y) ? x : y; } /* Returns the index of x if present, else returns -1 */ public static int fibonacciSearch(int arr[], int x, int n) { /* Initialize Fibonacci numbers */ int fibMMm2 = 0; // (m-2)'th Fibonacci number int fibMMm1 = 1; // (m-1)'th Fibonacci number int fibM = fibMMm2 + fibMMm1; // m'th Fibonacci number /* fibM is going to store the smallest Fibonacci Number greater than or equal to n */ while (fibM < n) { fibMMm2 = fibMMm1; fibMMm1 = fibM; fibM = fibMMm2 + fibMMm1; } // Marks the eliminated range from the front int offset = -1; /* While there are elements to be inspected. Note that we compare arr[fibMm2] with x. When fibM becomes 1, fibMm2 becomes 0 */ while (fibM > 1) { // Check if fibMm2 is a valid location int i = minimum(offset + fibMMm2, n - 1); /* If x is greater than the value at index fibMm2, cut the subarray array from offset to i */ if (arr[i] < x) { fibM = fibMMm1; fibMMm1 = fibMMm2; fibMMm2 = fibM - fibMMm1; offset = i; } /* If x is less than the value at index fibMm2, cut the subarray after i+1 */ else if (arr[i] > x) { fibM = fibMMm2; fibMMm1 = fibMMm1 - fibMMm2; fibMMm2 = fibM - fibMMm1; } /* Element found. Return index */ else return i; } /* Comparing the last element with x */ if (fibMMm1 == 1 && arr[n - 1] == x) return n - 1; /* Element not found. Return -1 */ return -1; } // Driver code public static void main(String[] args) { int arr[] = { 10, 22, 35, 40, 45, 50, 80, 82, 85, 90, 100, 235 }; int n = 12; int x = 235; int index = fibonacciSearch(arr, x, n); if (index >= 0) System.out.print("Element found at index: " + index); else System.out.print( x + " isn't present in the array"); } } // This code is contributed by sourabh_jain. # Pythin3 program of the above approach def fibonacci_search(arr, x, n): # Initialize Fibonacci numbers fibMMm2 = 0 # (m-2)'th Fibonacci No. fibMMm1 = 1 # (m-1)'th Fibonacci No. fibM = fibMMm2 + fibMMm1 # m'th Fibonacci # fibM is going to store the smallest # Fibonacci Number greater than or equal to n while fibM < n: fibMMm2 = fibMMm1 fibMMm1 = fibM fibM = fibMMm2 + fibMMm1 # Marks the eliminated range from the front offset = -1 # while there are elements to be inspected. # Note that we compare arr[fibMm2] with x. # When fibM becomes 1, fibMm2 becomes 0 while fibM > 1: # Check if fibMm2 is a valid location i = min(offset + fibMMm2, n - 1) # If x is greater than the value at # index fibMm2, cut the subarray array # from offset to i if arr[i] < x: fibM = fibMMm1 fibMMm1 = fibMMm2 fibMMm2 = fibM - fibMMm1 offset = i # If x is less than the value at # index fibMm2, cut the subarray # after i+1 elif arr[i] > x: fibM = fibMMm2 fibMMm1 = fibMMm1 - fibMMm2 fibMMm2 = fibM - fibMMm1 # element found. return index else: return i # comparing the last element with x if fibMMm1 and arr[n - 1] == x: return n - 1 # element not found. return -1 return -1 # Driver Code arr = [10, 22, 35, 40, 45, 50, 80, 82, 85, 90, 100, 235] n = len(arr) x = 235 index = fibonacci_search(arr, x, n) if index >= 0: print("Element found at index:", index) else: print(x, "isn't present in the array") # This code is contributed by sourabh_jain. // C# program of the above approach using System; class GFG { // Function to find the minimum of two elements public static int Min(int x, int y) { return (x <= y) ? x : y; } /* Returns the index of x if present, else returns -1 */ public static int FibonacciSearch(int[] arr, int x, int n) { /* Initialize Fibonacci numbers */ int fibMMm2 = 0; // (m-2)'th Fibonacci number int fibMMm1 = 1; // (m-1)'th Fibonacci number int fibM = fibMMm2 + fibMMm1; // m'th Fibonacci /* fibM is going to store the smallest Fibonacci Number greater than or equal to n */ while (fibM < n) { fibMMm2 = fibMMm1; fibMMm1 = fibM; fibM = fibMMm2 + fibMMm1; } // Marks the eliminated range from the front int offset = -1; /* While there are elements to be inspected. Note that we compare arr[fibMm2] with x. When fibM becomes 1, fibMm2 becomes 0 */ while (fibM > 1) { // Check if fibMm2 is a valid location int i = Min(offset + fibMMm2, n - 1); /* If x is greater than the value at index fibMm2, cut the subarray array from offset to i */ if (arr[i] < x) { fibM = fibMMm1; fibMMm1 = fibMMm2; fibMMm2 = fibM - fibMMm1; offset = i; } /* If x is less than the value at index fibMm2, cut the subarray after i+1 */ else if (arr[i] > x) { fibM = fibMMm2; fibMMm1 = fibMMm1 - fibMMm2; fibMMm2 = fibM - fibMMm1; } /* Element found. Return index */ else return i; } /* Comparing the last element with x */ if (fibMMm1 == 1 && arr[n - 1] == x) return n - 1; /* Element not found. Return -1 */ return -1; } // Driver code public static void Main() { int[] arr = { 10, 22, 35, 40, 45, 50, 80, 82, 85, 90, 100, 235 }; int n = 12; int x = 235; int index = FibonacciSearch(arr, x, n); if (index >= 0) Console.Write("Element found at index: " + index); else Console.Write(x + " isn't present in the array"); } } // This code is contributed by sourabh_jain. // JavaScript program of the above approach /* Returns the index of x if present, else returns -1 */ function fibonacciSearch(arr, x, n) { /* Initialize Fibonacci numbers */ let fibMMm2 = 0; // (m-2)'th Fibonacci No. let fibMMm1 = 1; // (m-1)'th Fibonacci No. let fibM = fibMMm2 + fibMMm1; // m'th Fibonacci /* fibM is going to store the smallest Fibonacci Number greater than or equal to n */ while (fibM < n) { fibMMm2 = fibMMm1; fibMMm1 = fibM; fibM = fibMMm2 + fibMMm1; } // Marks the eliminated range from the front let offset = -1; /* While there are elements to be inspected. Note that we compare arr[fibMm2] with x. When fibM becomes 1, fibMm2 becomes 0 */ while (fibM > 1) { // Check if fibMm2 is a valid location let i = Math.min(offset + fibMMm2, n - 1); /* If x is greater than the value at index fibMm2, cut the subarray array from offset to i */ if (arr[i] < x) { fibM = fibMMm1; fibMMm1 = fibMMm2; fibMMm2 = fibM - fibMMm1; offset = i; } /* If x is less than the value at index fibMm2, cut the subarray after i+1 */ else if (arr[i] > x) { fibM = fibMMm2; fibMMm1 = fibMMm1 - fibMMm2; fibMMm2 = fibM - fibMMm1; } /* Element found. Return index */ else return i; } /* Comparing the last element with x */ if (fibMMm1 && arr[n - 1] == x) { return n - 1; } /* Element not found. Return -1 */ return -1; } /* Driver code */ let arr = [10, 22, 35, 40, 45, 50, 80, 82, 85, 90, 100, 235]; let n = arr.length; let x = 235; let index = fibonacciSearch(arr, x, n); if (index >= 0) { console.log("Element found at index: " + index); } else { console.log(x + " isn't present in the array"); } // This code is contributed by sourabh_jain. <?php // PHP program of the above approach /* Returns the index of x if present, else returns -1 */ function fibonacciSearch($arr, $x, $n) { /* Initialize Fibonacci numbers */ $fibMMm2 = 0; // (m-2)'th Fibonacci No. $fibMMm1 = 1; // (m-1)'th Fibonacci No. $fibM = $fibMMm2 + $fibMMm1; // m'th Fibonacci /* fibM is going to store the smallest Fibonacci Number greater than or equal to n */ while ($fibM < $n) { $fibMMm2 = $fibMMm1; $fibMMm1 = $fibM; $fibM = $fibMMm2 + $fibMMm1; } // Marks the eliminated range from the front $offset = -1; /* While there are elements to be inspected. Note that we compare arr[fibMm2] with x. When fibM becomes 1, fibMm2 becomes 0 */ while ($fibM > 1) { // Check if fibMm2 is a valid location $i = min($offset + $fibMMm2, $n - 1); /* If x is greater than the value at index fibMm2, cut the subarray array from offset to i */ if ($arr[$i] < $x) { $fibM = $fibMMm1; $fibMMm1 = $fibMMm2; $fibMMm2 = $fibM - $fibMMm1; $offset = $i; } /* If x is less than the value at index fibMm2, cut the subarray after i+1 */ elseif ($arr[$i] > $x) { $fibM = $fibMMm2; $fibMMm1 = $fibMMm1 - $fibMMm2; $fibMMm2 = $fibM - $fibMMm1; } /* Element found. Return index */ else return $i; } /* Comparing the last element with x */ if ($fibMMm1 == 1 && $arr[$n - 1] == $x) return $n - 1; /* Element not found. Return -1 */ return -1; } /* Driver code */ $arr = array(10, 22, 35, 40, 45, 50, 80, 82, 85, 90, 100, 235); $n = count($arr); $x = 235; $index = fibonacciSearch($arr, $x, $n); if ($index >= 0) printf("Element found at index: " . $index); else printf($x . " isn't present in the array"); ?> // This code is contributed by sourabh_jain. Time Complexity: O(log(n)) Using Fibonacci Search
Auxiliary Space: O(1) Using Fibonacci Search
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